Structural, thermodynamic, and magnetic properties of SrFe12O19 hexaferrite modified by co-substitution of Cu and Gd

A hard magnetic system of SrFe12O19 nanomaterial was modified according to the composition of Sr0.95Gd0.05Fe12−xCuxO19 with x = 0.0, 0.30, and 0.60 using the sol–gel technique. The structures of the samples were evaluated using X-ray diffraction (XRD) along with Rietveld refinement, and an M-type hexaferrite with a hexagonal structure was confirmed with a trace amount of the α-Fe2O3 phase. In addition, transmission electron microscopy (TEM) analysis revealed polycrystalline nanoplates in all samples. Furthermore, the bond structures of the octahedral and tetrahedral sites along with the thermodynamic properties of these ferrites were extracted from the FTIR spectra at room temperature. The Debye temperature (θD) decreased from 755.9 K to 749.3 K due to the co-substitution of Gd3+ at Sr2+ and Cu2+ at Fe3+. The magnetic hysteresis (M–H) measurements revealed that the coercivity decreased from 5.3 kOe to 1.5 kOe along with the highest magnetization saturation (Ms) of 65.2 emu g−1 for the composition Sr0.95Gd0.05Fe11.7Cu0.3O19, which is suitable for industrial application. The effect of local crystalline anisotropy in magnetization was explored using the law of approach to saturation (LAS). Finally, thermo-magnetization was recorded in the range from 400 K to 5 K for cooling under zero field and in the presence of a 100 Oe field, and magnetic transitions were tracked due to the introduction of the foreign atoms of Gd and Cu into SrFe12O19.


Introduction
M-type Sr-hexaferrite (SrFe 12 O 19 ), SFO, was rst discovered in the Philips research laboratory 1 and due to its hard magnetic properties and chemical stability, along with cost-effective production, it has attracted a lot of attention. 2As hard magnetic materials, there are numerous engineering uses for M-type hexagonal ferrites, MFe 12 O 19 (where M = strontium (Sr), barium (Ba) and lead (Pb)), including magnetic recording media, microwave devices, and high-frequency applications. 3he hexaferrite structure can be divided into three basic block sequences, namely, spinel (Fe 6 O 8 ) 2+ , hexagonally packed (SrFe 6 O 11 ) 2− -R block, and SRS*R* block, which are divided into the following types: M, Z, Y, W, X, and U. 4 The strontium hexaferrite (SrFe 12 O 19 ) crystallizes with a hexagonal magneto-plumbite structure and belongs to the space group P6 3 /mmc.5 The 24 Fe 3+ atoms in the unit cell are spread among ve different places in the hexagonal structure, which has two chemical units.Fig. 1 shows three octahedral symmetry sites (12k, 2a, and 4f2), one bipyramidal site (2b), and one tetrahedral symmetry site (4f1).The magnetic characteristics of M-hexaferrite depend on the orientation of the magnetic moment in the sub-lattices. 6 A lot of research was carried out regarding its advantageous magnetic properties such as magnetic saturation, magnetic hardness, and Curie temperature.The magnetism of hexaferrite is strongly inuenced by shape, magneto-crystalline anisotropy, and average crystallite size.7 Since a few decades ago, M-type hexaferrites have been used to replace rare earth (Nd, Gd, Ho, etc.) and d-block (Co, Ti, Ni, Cu, Mn, etc.) elements to enhance the magnetic and dielectric properties.8 The doping or substitution of foreign elements in the structure of M-type strontium hexaferrites enhances the magnetic behavior, absorption of microwaves, quality, ferromagnetic resonance frequency, and so on.Numerous investigations with a similar focus were carried out, and one of them found that bimetallic La-Co substitution was the best way to increase magnetocrystalline anisotropy without altering saturation magnetization M s .9 According to the Gorter model, 10 the superexchange interactions via O 2 anions couple sixteen ferric ion moments of magnetic attraction (12k, 2a, and 2b) parallel to the c-axis, resulting in ferrimagnetic ordering. Te outcomes of rstprinciples calculations on magnetic structure have veried the concept.Andrzej Hilczer 6 examined how doping with Sc affected the coercivity, remanence, and dielectric properties of SrM hexaferrites.Shakoor et al. added Bi-Cr to the strontium hexaferrites with interesting results and reported 11 that according to the XRD data, the material contains a single magnetoplumbite phase, and the crystallite size ranges from 41 to 57 nm.The isolated disadvantage of La-Co and Bi-Cr-replaced M-type ferrites is the cost associated with the adding process, which uses pricey metals like La and Bi. Iense research is being done on these materials since it is still challenging to create low-cost ferrites with improved magnetic properties.10,12 M. Elansary et al. 13 reported the effects of doping Gd 3+ , Sm 3+ , and transition elements (M = Ni, Zn, Mn, and Mg) on the structural, magnetic, and morphological properties of Sr 0.9 M 0.1 Fe 11.98 Sm 0.01 Gd 0.01 O 19 .The nanoparticles with the composition BaFe 12−3x Gd x Sm x Y x O 19 for x = 0, 0.01, 0.02 were synthesized by I. Lisser et al. 14 using the sol-gel autocombustion method.In addition, a single-phase hexaferrite of composition Sr (1−x) La x Gd y Sm z Fe (12−(z+y)) O 19 (x = 0.3, y = z = 0.01) was synthesized by the same method 15 and the sizes of the particles were observed to vary from 53 nm to 46 nm.A ternary dopant, Gd-Ho-Sm, was implemented to synthesize a single phase of M-type Sr hexaferrite of 49 nm particles in a costeffective way.16 It has been reported that Gd 3+ and Ho 3+ ions have strong preferences towards the 12k site, whereas the Sm 3+ ions prefer to occupy the 2A site of the lattice.Another sample of Al-SFO exhibited good catalytic activity compared to the parent compound due to the presence of Al 3+ ions in the octahedral sites, and these sites are exposed to the surface of the strontium hexaferrite catalyst.17 Moreover, catalytic activity could be induced in the hard magnetic strontium hexaferrite sample by replacing the small fraction of Fe with Cu. 18,19 Therefore, SrFe 12 O 19 powders of various forms and sizes have been made using a variety of procedures, including the sol-gel, hydrothermal, co-precipitation of chemicals, solid-state reaction, and micro-emulsion approaches, among others.One of the practical ways to crystallize the hexaferrite phase at a comparatively lower annealing temperature is to create SrFe 12 O 19 nanoparticles (NPs) using the sol-gel process.12 Sol-gel technology is extensively used as a great way to create nanospinels because of its advantages of low processing costs, energy efficiency, high production rates, and the production of ne homogeneous powder.11 Incorporating metallic ions like Gd 3+ and Cu 2+ into the hexaferrite has produced some interesting outcomes.Cu 2+ prefers to occupy the octahedral 4f2 position, which has a downspin state and contributes adversely to the overall saturation magnetization.20 However, the addition of any foreign elements to Sr hexaferrites not only improves their physical properties, but different types of anisotropy may also develop inside, which limits their applications.
The present work includes an in-depth investigation of the structural, thermodynamic, magneto-anisotropic, and thermomagnetic properties of SrFe 12 O 19 nanoparticles modied by the co-substitution of a rare earth element, Gd 3+ , at Sr 2+ and a transition element, Cu 2+ , at Fe 3+ .

Sample preparation
The M-type hexaferrite, SrFe 12 O 19 (parent sample), was modi-ed by the substitution of Gd at Sr, and Cu at Fe, and the compositions of Sr 0.95 Gd 0.05 Fe

Characterization
The thermal stability of the as-prepared parent sample, SFO, was conrmed and differential thermal analysis (DTA) and thermogravimetric (TG) measurements were performed in a PerkinElmer STA-8000 °C system at a heating rate of 10 K min −1 under a nitrogen (N 2 ) atmosphere.The structures of SFO, SGFCO-1 and SGFCO-2 samples were evaluated using an Xray diffractometer (PW3040) with Cu-K a radiation (l = 1.5405Å) and the diffraction patterns were recorded in the range of 20°# 2q # 70°at room temperature (RT = 300 K).The microstructures of the studied samples, along with selected area diffraction patterns (SAED), were determined using a Tecnai G2 30ST transmission electron microscope (TEM).Elemental studies of the synthesized samples were conducted using an energydispersive X-ray spectrometer (EDS) attached to the TEM and the measurements were performed for 5 different locations of the overall microstructure.Moreover, the bond structure and thermodynamic properties of all samples were evaluated by Fourier transform infrared spectroscopy (FTIR) on a Nicolet NEXUS 470 FTIR Spectrometer in the range of 350-3700 cm −1 at RT. Finally, the magnetic hysteresis (M-H loop) at RT and magnetization as a function of temperature (M-T) ranging from 10 K to 400 K were determined for all studied samples using a Quantum Design PPMS.For the M-H loop measurement, the highest limit of the magnetic eld (H) was ±20 kOe and for the M-T measurement, the rate of cooling (dT/dt) was 2 K s −1 .

Thermal stability
The thermogravimetric (TG) and differential thermal analysis (DTA) of the as-prepared SrFe 12 O 19 sample ensured the formation and phase stability of the synthesized sample.Fig. 2 displays the TG and DTA curves between RT and 1000 K for the parent SFO sample and the decomposition of the ingredients was observed due to a thermally activated chemical reaction.However, this decomposition followed several steps at elevated temperatures and the rst step of 6.8% weight loss was observed between RT and 415 K, which was attributed to a trace quantity of chelating compound with ammonia.Upon further heating to 810 K, the evaporation of the remaining solvent and the crystallization process were ascribed to a considerable weight loss of 8.7% as a second step.Beyond that, a nal step of 0.9% weight loss was observed up to 1000 K and 83.6% residue remained aer thermal analysis in the overall temperature range.Two endothermic peaks at 360 K and 760 K are likely due to water loss and Sr 2+ and Fe 2+ decomposition, respectively.This demonstrates the thermal stability of the synthesized SFO hexaferrite NPs.  3. The arrangements of diffraction patterns ensure the formation of the crystalline phase in all the samples.Therefore, the crystallographic planes and structural parameters along with the phase fractions were extracted from the analysis of XRD data using the Rietveld renement method by FullProf Suite soware. 21,22Fig. 3 shows the tting of diffraction patterns, where the experimental data (I Obs ) are depicted by the red circles, the black lines represent calculated intensities (I Cal ), and the blue lines represent (I Obs − I Cal ).The Bragg positions are displayed by the green and orange vertical lines.Here, the quality-based tting of XRD data has been determined by c 2 , which is between 2.35 and 5.54.The other tting factors are R p (residual of least squares renement) and R wp (weighted prole factor), which are also limited.From the analysis of the XRD peak matching, a major part of the patterns matches the P6 3 / mmc space group, while few of them t the R 3c space group, which indicated the presence of two identical phases inside the synthesized samples.However, the respective arrangements of the odd/even lattice peaks of (110), ( 112  mmc space group (JCPDS Card No. 79-1411). 12The other phase includes the arrangements of the odd/even lattice peaks of (012), ( 104), ( 113), ( 024), ( 211), ( 018), (224), which are reected from the a-Fe 2 O 3 of the rhombohedral structure from the R 3c space group (JCPDS Card No. 33-0664). 23However, from close observation of the patterns, the elimination of the impurity phase (a-Fe 2 O 3 ) is due to the co-substitution of Gd and Cu in the parent SFO sample.Apart from this, the structural parameters have been included in Table 1.The obtained experimental values of the lattice constants were a = b = 5.8761 Å and c = 23.0239Å for the parent SFO sample, and the reported values for the same composition were 5.8751 Å and 23.0395 Å, respectively, 24 where the synthesis conditions are responsible for the differences.However, the lattice parameters for the major phase increased due to the substitution of Gd 3+ at Sr 2+ and Cu 2+ at the place of Fe 3+ , but the variation is very marginal in a, b and c.The ionic radius of Gd 3+ (93.8 pm) is smaller than that of Sr 2+ (118 pm) for a coordination number of six, according to the database of ionic radii provided by R. D. Shannon. 25herefore, the lattice parameters (a, b and c) are supposed to decrease in SGFCO due to the substitution of Gd 3+ at Sr 2+ .On the other hand, the ionic radius for Cu 2+ (73 pm) is larger than Fe 3+ (64.5 pm) for a coordination number of six. 25 Consequently, the lattice parameters (a, b and c) are supposed to increase in SGFCO due to the substitution of Cu 2+ at Fe 3+ .Since the substitution of Cu 2+ is greater than Gd 3+ in the parent sample, the lattice parameters increased.However, the increase is marginal even though more Cu was substituted in the SGFCO sample.The overall variations increased the unit cell volume (V) in the SGFCO-1 and SGFCO-2 samples.The percentage of the existing phases, W P (%) was determined from equation: 22

Structural characterization
where the parameters of the unit cell volume (V), the formula unit of the unit cell (Z), formula unit mass (M) and scale factor (S) were determined from the Rietveld renement.°C.On the other hand, the melting point of Gd is 1084 °C, whereas the melting point of Sr is 768.8 °C.Therefore, the replacement of Gd at Sr led to an increase in the phase formation temperature.As a result, the mutual effect of the cosubstitution of Cu and Gd created a complex situation during the phase formation of the pure hexaferrite phase of SrFe 12 O 19 .From the viewpoint of Cu substitution only, the hexaferrite phase of SrFe 12 O 19 achieved a more favourable environment from the calcination temperature of 750 °C.Therefore, a low rate of secondary phase was observed in the SGFCO-1 sample and a further decrease in the amount (%) was observed due to the replacement of more Fe by Cu atoms (SGFCO-2).Finally, sample SGFCO-2 with a smaller amount of the a-Fe 2 O 3 phase (17.9%) showed the highest value of the lattice parameter as compared to the other two samples since a smaller amount of Fe 3+ departed from the parent phase to form the secondary phase of the a-Fe 2 O 3 phase.
This discrepancy in the phase amounts will affect the other physical properties, including the magnetic properties, of the synthesized samples.Moreover, other structural factors like Paper RSC Advances crystallite sizes and porosities also play a vital role in the enhancement of the ferromagnetic behaviour of the ferrite samples. 29,30The sizes of crystallites (d 114 ) in all studied samples were estimated from the diffraction peak at (114), which represents the major phase (hexagonal) and calculation was performed by the Debye-Scherrer formula 31 as expressed by the following equation: where b 114 is the FWHM determined by the Gaussian tting of the peak (114) at the Bragg position of q 114 , l = 1.5418Å (wavelength of Cu-k a radiation) and k = 0.9 (a dimensionless constant).The micro-strain (3) of these crystallites was calculated using the following equation: The obtained values of d 114 and 3 for all studied samples are included in Table 1 and marginal variations in the crystallite size of the major phase were observed.

Morphological analysis
The microstructures along with grain size distribution for SFO, SGFCO-1 and SGFCO-2 samples were observed using transmission electron microscopy (TEM) and Fig. 4

Elastic properties and thermal behaviour
The elastic and thermodynamical properties of the SrFe  7 shows the FTIR spectra obtained for the studied samples in the wavenumber range 350-3600 cm −1 .Here, the absorption peaks at nearly 600 cm −1 and 447 cm −1 represent the main characteristic features of the synthesized samples, which are denoted by n A and n B , respectively.The bands at around 600 cm −1 and 447 cm −1 originated due to oxygen motion at the tetrahedral (A-site) and octahedral (B-site) sites, respectively for the studied ferrites. 32The small band n 0 1 ; near 754 cm −1 , signies the vibration of metal ions in the crystal lattice. 33In the synthesized sample, the broad bands at around 1120 cm −1 and 3415 cm −1 are attributed to the stretching vibrations of the O-H group of citric acid and molecular water. 12The band at 856 cm −1 is attributed to SrCO 3 .The band at 1634 cm −1 is assigned to the stretching vibrational band of the C]O group of CA. 34 The band at around 1467 cm −1 corresponds to the vibrational modes of nitrate stretching. 35,36The C]C bond at 1388 cm −1 was observed due to the presence of CO 2 during the heat treatment process. 37The overall bands around 400-600 cm −1 ensured the formation of the hexaferrite phase 38 in all studied samples.However, a small vibrational band at 550 cm −1 is an indicator of the existing a-Fe 2 O 3 phase, 12 concomitant with the XRD data.The bond structure and force constants of the studied samples were extensively analysed from close observation of the absorption peaks n A and n B .The widths of these peaks were compared by the Gaussian tting (Fig. 7(b)).The widths of the peaks at the tetragonal and octahedral sites were denoted by W T and W O , respectively, and the values are included in Table 2. W T increased for both SGFCO-1 and SGFCO-2 samples, which implies that M-O bonds at the tetrahedral site are highly affected due to substitution of Gd 3+ at Sr 2+ and Cu 2+ at Fe 3+ .There was no peak shoulder at n B , conrming the presence of Fe 2+ from the octahedral site. 39The slight shiing of n A and n B to the lower wavenumber indicates the perturbation in the Fe 2+ -O 2− bond that occurred for Gd 3+ and Cu 2+ substitution. 40The general equation for the force constant (k) of the metal-oxygen bond can be expressed by the following equation: where y is the wave number, c is the velocity of light, and m is the effective mass.Eqn (4) has been used to measure the force constant of Fe-O bond at octahedral and tetrahedral sites and the effective mass for the bond is m  Table 2 The estimated values of average grain size (X A ), internal porosity (P i ) (%), and therefore, the variation of force constants of the ions existing in tetrahedral and octahedral sites with FWHM of peaks at vibrational bands of octahedral (W O ) and tetrahedral (W T ) for SFO, SGFCO-1, and SGFCO-2 samples decreased for the cosubstitution of Gd 3+ and Cu 2+ in SFO, which is reected in the Fe-O bond length.Therefore, the overall force constants of M-O bonds at the octahedral site (k O ) and tetrahedral site (k T ) were determined from the following formulas: 42,43 k where M T and M O are the masses of the molecules at the tetrahedral and octahedral sites, respectively.The average cation-anion bond lengths in both sites were also estimated using the same formula, L ¼ ffiffiffiffiffiffiffiffiffiffi 17=k 3 p .The average force constant (k av ) was used to estimate the elastic constants in this case.From the lattice constant (a) and k av , the stiffness constant (C 11 = longitudinal modulus) was computed as C 11 = k av /a. 44For the pore fraction, Poisson's ratio (s) of the samples was calculated using the relation, s = 0.324 × (1 − 1.043f). 45,46The values of s exhibit a consistent divergence between 0.26 and 0.28 based on the compositions (Table 3) and the values fall within the range of −1 to 0.5, which is matched with the theory of isotropic elasticity.In addition, the stiffness constant C 12 was calculated from s and C 11 using the following equation: The acquired values of C 12 are positive and show the stability of the synthesized Gd-doped SFO hexaferrite.They range from 15.44 GPa to 15.88 GPa, depending on the compositions.The values of longitudinal elastic wave velocity (V L ) were determined using the following equation: 46 where r is the XRD density, as evaluated earlier.The change in V L with Gd 3+ replacement is presented in Table 3 and all the velocities are higher for the SGFCO-1 sample.In addition, the Debye temperature (q D ) is characteristic of a particular material that allows homogeneous isotropic massless phonons to dominate the thermal behavior of solids and it is the temperature at which phonons can have their highest frequency.The values of q D for the studied samples have been evaluated from the relation: 47,48 where ħ is Planck's constant, K B is Boltzmann's constant, c is the velocity of light, and n av is the average value of wavenumbers.The value of q D for SFO sample is 755.9K which decreases with the increase in Cu 2+ substitution.Table 3 represents the decrease in q D and longitudinal elastic wave velocity (V L ) due to Gd 3+ and Cu 2+ substitution.Here, the decrease in q D indicates that the lattice vibrations held up for Gd 3+ and Cu 2+ substitution.The decrease in q D may be associated with the increase in the conduction electron density N n (n-type).Hence, the density of conduction holes N p (p-type) decreases. 49On the contrary, Anderson's formula depicts the linear increase in q D with V m . 46owever, the synthesized SGFCO-1 ferrite sample is mostly porous, and anomalies were observed.

Magnetic hysteresis
The M-H loop of pure SrFe 12 O 19 and Sr 0.95 Gd 0.05 Fe 12−x Cu x O 19 (x = 0.30 and 0.60) nanoparticles are displayed in Fig. 8(a) and the shape of the loops represents the ferromagnetic behaviour of all studied samples.Fig. 8(c) displays the linear tting of M versus 1/H 2 in the higher region of H and the data follows the law of approach to saturation (LAS). 50The maximum levels of magnetization (M S ) of all samples were determined from the yintercept of the extrapolated line in Fig. 8(c).The variation of M s and coercivity (H c ) with Cu concentration has been depicted by the inset Fig. 8(a).Here, H c is inversely proportional to M S , which ensured the magnetic soening of the SFO due to Gd 3+ and Cu 2+ substitution and the values of M s reached a maximum of 65.2 emu g −1 , which is suitable for industrial application.The stability of the remanent state of magnetization is described by H c , which is a specic incoherent mode caused by the rotation of spontaneous magnetization.Table 3 Elastic properties of SFO, SGFCO-1, and SGFCO-2 showing Poisson's ratio (s), Zener anisotropy (Z A ), Debye temperature (q D ), Young's modulus (E), rigidity modulus (G), bulk modulus (K), elastic wave velocities for longitudinal (v L ), transverse (v T ) and mean velocity (v m ) Paper RSC Advances and SGFCO-2 samples are, respectively, 1.9 kOe and 1.5 kOe, which are much lower as compared to the SFO sample (5.3 kOe).This indicates the decrease in magnetic anisotropy due to the substitution of Gd 3+ at Sr 2+ and Cu 2+ at Fe 3+ . 51,52owever, the net magnetization (n B ) was determined from M s and the molecular mass (M) of the studied samples according to the following equation: Table 4 displays the values of n B and an increased net magnetization was achieved due to the substitution of Gd 3+ at Sr 2+ and Cu 2+ at Fe 3+ in the SFO sample.Here, the partial substitution of Gd 3+ at Sr 2+ led to an increase in the net magnetization as the magnetic moments of Gd 3+ (8 mB) and Fe 2+ (4.9 mB) at tetrahedral sites are greater than that of Fe 3+ (5.9 mB). 54On the other hand, as the magnetic moment of Cu 2+ (1.73 mB) is lower than that of Fe 3+ (5 mB), Cu 2+ substitution at Fe 3+ should lead to the lowering of the net magnetization of SGFCO-1 and SGFCO-2 samples.However, these samples showed higher magnetization than the parent sample (SFO), which is attributed to the site preference of Cu 2+ ; as suggested in the literature, 55 Cu 2+ preferably occupies an octahedral site.In the M-type hexaferrite, the magnetic moments of Fe are located at the three octahedral (2a, 12k, and 4f2) sites that are parallel to each other, and these moments are coupled in an antiparallel manner to the magnetic moments of Fe located at the tetrahedral (4f1) and trigonal bipyramidal (2b) sites.The magnetic moments within the 4f1 and 2b sites are also parallel to each other.Therefore, the net magnetization arises due to the difference between the magnetization of the octahedral sites (2a, 12k, and 4f2) and the net magnetization of both the tetrahedral and trigonal bipyramidal sites (4f1 and 2b).Since Cu 2+ prefers to occupy the octahedral site, replacing the Fe 3+ , then the net magnetization of the octahedral sites decreases.From a literature review by P. N. Anantharamaiah et al., it was observed that Cu 2+ replaces the Fe 3+ of the 4f2 site with an equivalent amount. 56Therefore, the substitution of Cu 2+ takes part in increasing the net magnetization (n B ) in SGFCO-1 and SGFCO-2.Besides, the squareness ratio (S r = M r /M S ) determines the uniaxial anisotropy contribution in RE-doped nanoparticles generated by the internal strains. 57,58The values of S r are less than 1 for the studied samples and indicate the presence of an isolated ferromagnetic single domain 59 .The squareness ratio M r /M s determines the domain state.It can be used to distinguish between single domain (SD), multidomain (MD), and pseudo-single domains (PSD).Indeed, the material can be considered as MD for M r /M s < 0.1, where the magnetization change can be achieved by the domain wall movement in relatively low elds, contrarily to SD (M r /M s > 0.5) where the changes in the magnetization can be realized by its rotation. 60Besides, the material can be considered as PSD if M r /M s is between 0.1 and 0.5. 61onsequently, the synthesized SGFCO-1 sample falls into PSD as M r /M s = 0.5, while the other two samples fall into the SD as M r /M s > 0.5.Moreover, M r /M s is linked to the magnetic anisotropy and super-exchange interaction between Table 4 The effects of Cu 2+ substitution on the magnetic properties showing maximum magnetization (M s ), coercivity (H c ), remanence (M r ), magnetic moment (n B ), squareness ratio (S r ) and calculated maximum product, (BH) max for SFO, SGFCO- tetrahedral (A) and octahedral (B) ions in the spinel lattice, which depends on the type and number of ions at A and B sites.This distribution affects the magnetization and coercivity of A and B sub-lattices. 62The variation in the cationic distribution of Fe 2+ and Fe 3+ due to the substitution of Gd 3+ at Sr 2+ and Cu 2+ at Fe 3+ is the main reason for the gradual variation in M r /M s for the synthesized ferrites.However, some Fe 3+ exits the spinel lattice due to the formation of the impurity phase of a-Fe 2 O 3 , though the cationic distribution is ruled by the foreign atoms of Cu and Gd in SGFCO-1 and SGFCO-2.Therefore, the M r /M s ratio decreases in SGFCO-1 and then increases in SGFCO-2, depending on the amount (%) of the a-Fe 2 O 3 phase.The maximum energy density product (BH) max for the studied samples was calculated from the equation 63 as follows: where m o is the permeability constant (m o = 4p × 10 −7 H m −1 ).The values of (BH) max have been included in Table 4 and the maximum value was obtained for the SGFCO-2 sample (1.33 MGOe).It was previously reported that an excess amount of a-Fe 2 O 3 , which remained unreacted, could lead to the weakening of the magnetic properties. 64However, in our case, the amount of a-Fe 2 O 3 decreased due to the substitution of Gd 3+ and Cu 2+ in the SFO sample and (BH) max increased from 0.24 MGOe to 1.33 MGOe, and M s increased from 27.6 to 65.2 emu g −1 .

Magnetic anisotropy
The magnetic properties of any ferrite samples are dependent on their local crystalline anisotropy.Therefore, the M-H curves of the studied samples were tted by the empirical formula of LAS theory, and the equation is expressed as follows: 65 where A is the inhomogeneity parameter, B is the anisotropy factor and c p denes the high eld susceptibility.In addition, A/H describes the degree of material inhomogeneity while x p H denes the term for forced magnetization caused by the applied eld.The terms of c and A/H vanished for the application of an excessive magnetic eld.Another term, B H 2 ; is connected to the magneto-crystalline anisotropy parameter.Therefore, the M-H data of Fig. 8(a) has been tted by eqn (12)  for a specic region of H (6-20 kOe) and the ttings are depicted in Fig. 9.The values of the statistical coefficient (R 2 ) conrmed the tting quality with a high degree of stability.The measured values of A, B and c p along with R 2 have been included in Table 5.Here, the higher values of the inhomogeneity parameter (A) are attributed to the presence of structural defects due to the presence of any secondary phase. 66In our present samples, a-Fe 2 O 3 is the secondary phase as predicted from XRD and FTIR spectra and this phase creates nonmagnetic ion inclusions, as well as structural defects.Moreover, the anisotropy factor, B, can be determined from the following equation: where, K eff is the magneto-crystalline anisotropy constant, and H A is the anisotropy eld.Aer simplifying eqn (13), the value of H A and K eff can be determined from the following equations: The values of H A and K eff are included in Table 5.Here, the deduced H A showed fewer variations for substituted Gd 3+ and Cu 2+ .The overall variation in the magnetic parameters is depicted in Fig. 10.

Temperature-dependent magnetic properties
The thermo-magnetization (M-T) ranging from 10 K to 400 K for SFO, SGFCO-1 and SGFCO-2 is represented in Fig. 11.Here, the measurements were performed under the application of a 100 Oe applied eld and the magnetic properties were in the eld cooled cooling (FCC) mode between 400 K to 5 K.In addition, the M-T measurement in the zero-eld cooling (ZFC) mode was also measured for the studied samples in the same temperature range.From these M-T curves, the magnetic moment (emu g −1 ) was higher for the SGFCO-1 and SGFCO-2 samples in the whole temperature run, which is concomitant with the magnetic hysteresis for the 100 Oe applied eld.In addition, the magnetization during FCC measurement was increased by lowering the temperature for all studied samples except for a slight saltation for SFO and SGFCO-1 samples.The same type of behaviour was observed for the SrFe 12 O 19 samples by Gang Qiang 67 for the 50 Oe applied eld.The primary distinction between ZFC and FCC is whether an external magnetic eld is dominating throughout the cooling process.In addition, both methods together offer to explain the magnetic interactions in the SFO hexaferrite and different transitions can be identied in the thermal evolution of magnetization.Therefore, transition temperatures have been tracked from the rst derivative of magnetization (dM/dT) of ZFC and FCC data.The variation of (dM/dT) with temperature (T) is illustrated by the inset in Fig. 11(a-c); a jump was observed at ∼145 K in all samples.This peak approximates the temperature of the Verwey transition (T V ∼ 120 K) of Fe 3 O 4 , which is a rst-order magnetic phase transition related to the change in the magneto-crystalline anisotropy and the ordering of Fe 3+ and Fe 2+ ions at the octahedral sites 68 of the cubic spinel structure.Above this temperature, another jump in dM/dT was observed in all samples as illustrated in the inset of Fig. 11(a-c).Due to the presence of a-Fe 2 O 3 , a magnetic transition (weak ferromagnetic to antiferromagnetic) may occur at ∼260 K.This transition temperature is known as the Morin temperature (T M ) 68 and it varies with particle shape, size, and crystallinity.The values of T M were observed near 239 K, 355 K and 268 K for SFO, SGFCO-1 and SGFCO-2, respectively.Apart from this, the rare earth moments of Gd are responsible for the higher magnetic potential energy.As the temperature drops to a certain level of separation, the potential energy of the metastable state takes place with an orientation that switches the Gd moments in the opposite direction.Furthermore, the interaction between the adjacent Fe ions builds up a metastable state at a certain level of temperature and the moments of the Fe 3+ ions changed direction for a short time.Therefore, the huge magnetic potential energy might be released around the transition temperature in the SGFCO-1 sample, resulting in a decrease in the magnetization.However, with the increase in Cu 2+ content for the FCC mode, Table 5 Values of anisotropy factors (A and B), magnetic saturation from LAS fitting (M s1 ) high field susceptibility (c p ), anisotropy field factor (H A ), and magneto-crystalline anisotropy (K eff ) along with goodness of the curve fit (R 2 ) calculated from the fitting of M-H data (Fig. 6 the jumping behaviour nearly disappeared as seen in Fig. 11(c) for the SGFCO-2 sample.In principle, the measurement of FCC is dominated by both temperature and external magnetic eld, while in the ZFC mode, only the magnetic potential energy develops as the temperature is lowered.Thus, the creation and annihilation of the metastable state in ZFC is solely dominated by the temperature; in contrast in the FCC mode, the diminishing of the metastable state is due to the external magnetic eld responsible for the disappearance of jumping behaviour.Therefore, the ZFC/FC tests for the M-type hexaferrite systems revealed interesting behaviour due to the co-substitution of Gd and Cu and detected magnetic transition nature.

Conclusion
The Cu-Gd-substituted M-type Sr hexaferrites with the formula Sr 0.95 Gd 0.05 Fe

Fig. 1 A
Fig. 1 A diagram of the M-type hexaferrite structure for Fe 3+ ions arranged in five different positions.
The X-ray diffraction (XRD) patterns for the synthesized SrFe 12 O 19 , Sr 0.95 Gd 0.05 Fe 11.4 Cu 0.6 O 19 , and Sr 0.95 Gd 0.05 Fe 11.7 -Cu 0.3 O 19 were recorded at RT and the patterns are shown in Fig.

Fig. 3
Fig. 3 XRD patterns (I Obs ) recorded for the SrFe 12 O 19 and Sr 0.95 Gd 0.05 Fe 12−x Cu x O 19 compositions (x = 0.30 and 0.60) along with the calculated patterns (I Cal ), differences between the observed patterns and calculated patterns (I Obs − I Cal ) and peak positions (vertical bar) obtained by Rietveld refinement.

Fig. 4
Fig. 4 Microstructures obtained from transmission electron microscopy (TEM) showing (a) grain morphologies, (b) EDS spectra, (c) ring-type SAED patterns and (d) fast Fourier transform (FFT) patterns that demonstrate the poly-crystalline structure of the SrFe 12 O 19 sample.

Fig. 8
Fig. 8 (a) M-H loops for SrFe 12 O 19 , Sr 0.95 Gd 0.05 Fe 11.4 Cu 0.6 O 19 , and Sr 0.95 Gd 0.05 Fe 11.7 Cu 0.3 O 19 samples; (b) the inset shows the variations of M s and H c with doping Cu content in the parent composition.(c) Linear fitting of the variation of M versus 1/H 2 curve.
12−x Cu x O 19 for x = 0.30, 0.60 were synthesized.The raw materials of analytical grade strontium nitrate [Sr(NO 3 ) 2 ] and gadolinium nitrate [Gd(NO 3 ) 2 $5H 2 O] were obtained from LOBA Chemise, ferric nitrate [Fe(NO 3 ) 2 $9H 2 O] from E. Merck, and copper nitrate [Cu(NO 3 ) 2 $5H 2 O], 99.9% from ALDRICH.In addition, citric acid [C 6 H 8 O 7 $H 2 O] of 99% purity, from E. Merck and HCl were used as chelating agents.The stoichiometric amounts of 0.190 g (0.03 M) Sr(NO 3 ) 2 , 4.3632 g (0.03 M) Fe(NO 3 ) 2 $9H 2 O and 0.190 g (0.03 M) C 6 H 8 O 7 $H 2 O (1 : 12 : 1 for Sr, Fe and citrate) were dissolved at a room temperature in 30 ml distilled water (98%) for 2 h to manufacture undoped SrFe 12 O 19 .Aer that, the solution was evaporated using a water bath to speed up the gelation process.The dehydration process was performed over 6 hours, and aer that, a ne dried gel was produced over 24 hours in ovens set at 400 K. Through intermediate grinding, the dried gel of the components was nely mixed with oxides.Both SrFe 12 O 19 and doped powder samples were obtained aer calcination at 1023 K in a furnace.In this investigation, the synthesized SrFe 12 O 19 was identied as SFO.The other two compositions of Sr 0.95 -Gd 0.05 Fe 11.4 Cu 0.6 O 19 , and Sr 0.95 Gd 0.05 Fe 11.7 Cu 0.3 O 19 are presented herein as SGFCO-1 and SGFCO-2, respectively.

Table 1
28 for the replacement of Sr 2+ by Gd3+, and Fe 3+ by Cu2+with an amount of 5% in both cases.Here, the synthesized powder samples were calcined at 1023 K (750 °C) and the presence of a secondary phase of hematite (a-Fe 2 O 3 ) indicates an incomplete reaction.The reported minimum energy required to transform the oxide compounds SrO and Fe 2 O 3 , to produce the SrFe 12 O 19 phase was in the temperature range of 711-878 °C.26In another article by H. M. Shashanka et al., the single-phase Srhexaferrite was produced with a calcination temperature of 1200 °C for 2 h.27In an earlier report by M. A. Urbano Peña et al.,28a secondary phase of a-Fe 2 O 3 was observed in SrFe 12 O 19 samples calcinated at 800 °C and the samples were synthesized by the Pechini method.Therefore, the presence of a secondary phase (a-Fe 2 O 3 ) in pure SrFe 12 O 19 depends not only on the calcination temperature but also on the synthesis conditions and the presence of catalysts in the reaction environment.Moreover, the replacement of Cu at Fe in SrFe 12 O 19 led to a decrease in the phase formation temperature as the melting point of Cu is 1312 °C, whereas the melting point for Fe is 1535 presents the number of phases (%) in the studied samples and the impurity phase, a-Fe 2 O 3 , decreased from 27.2% to 17.
3 O 19 were determined from FTIR spectra obtained at RT. Fig.

Table 4
depicts the values of M S and H c .The values of H c for SGFCO-1 1, and SGFCO-2 samples ) for the M-type compositions SrFe 12 O 19 and Sr 0.95 Gd 0.05 Fe 12−x Cu x O 19 where x = 0.3 and 0.6 Fig. 10 The overall variation of magnetic parameters with Cu content for the M-type compositions of SrFe 12 O 19 , Sr 0.95 Gd 0.05 Fe 11.4 Cu 0.6 O 19 , and Sr 0.95 Gd 0.05 Fe 11.7 Cu 0.3 O 19 .
12−x Cu x O 19 (x = 0.30 and 0.60), were successfully prepared via the sol-gel method, and calcined at 750 °C in air for 4 hours.However, the substitution of Gd 3+ and Cu 2+ ions in SrFe 12 O 19 increased the unit cell volume and can eliminate the common impurity phase of a-Fe 2 O 3 .The grain sizes were also increased in the co-doped samples and varied from 20 nm to 100 nm holding the nano-plate shape.The saturation magnetization (M s ) increased with the introduction of Gd3+and Cu 2+ in SrFe 12 O 19 and M s was highest for Sr 0.95 Gd 0.05 Fe 11.4 Cu 0.6 O 19 (65.2 emu g −1 ) with the lowest coercivity (H c ) of 1.5 kOe as compared to the other two samples.Moreover, the increased number of magneto-crystalline anisotropic factors enabled this composition, resulting in a maximum energy density product, (BH) max , of 1.33 MGOe.The Sr 0.95 Gd 0.05 Fe 11.4 Cu 0.6 O 19 composition accumulated a huge magnetic potential energy and suppressed the magnetic transition.The overall properties of Sr 0.95 Gd 0.05 Fe 11.4 Cu 0.6 O 19 make it a strong contender for use in microwave-absorbing materials and high-density magnetic recording materials, multiple state logic, non-volatile memory and magnetoelectric sensors.